1. Field of the Invention
The present invention relates to a method for determining absolute density of a fluid, such as cement slurry, that typically contains entrained air. The term absolute density as used herein refers to the density of a fluid containing entrained air that would be theoretically obtained when measured at infinite pressure as if the entrained air was not present in the fluid. This method involves taking density measurements of the slurry at two different pressures and using these measurements to compute the absolute density of the slurry. This method is particularly designed to provide the operator with timely readings of absolute density that can then be used to control the production of the slurry to produce slurry of the desired air free density in a continuous slurry mixing operation, such as cement slurry needed in cementing an oil or gas well.
2. Description of the Related Art
All cement slurry has some air entrainment. The problem with air entrainment is that it affects the density measurement while mixing the slurry. Current technology densitometers can determine the slurry density accurately. The problem with this measurement is that the measurement includes the air that is in the slurry. After the slurry is pumped into the well, the pressure on the slurry becomes very high, maybe several thousand psi. This high pressure causes the entrained air to be compressed such that it no longer creates a void volume in the slurry. Thus, slurry that has entrained air at atmospheric pressure will have a density greater downhole than when it is measured at the surface.
This difference in slurry measurement can cause problems with completion of the cementing job because of the higher hydrostatic pressure at the bottom of the well due to the density difference and because of the higher viscosity of the slurry. After the air is compressed out of the slurry downhole, there is a smaller proportion of water in the slurry, thus creating a more viscous fluid. The higher viscosity causes a higher fiction pressure while pumping the slurry. This adds to the higher hydrostatic pressure to give a higher downhole pumping pressure. The higher pressure can cause loss of circulation and possible failure of the job.
This density measurement problem is further complicated by the fact that cement slurry contains three components: water, air, and a fixed dry blend of cement and additives that has an average absolute density. If cement slurry were composed of only two components, such as air and a liquid, the amount of entrained gases in that liquid mixture could be measured by methods such as the one taught in U.S. Pat. No. 6,598,457 which teaches a method for measuring entrained air in a two component, i.e. air and liquid, sample. However, because cement slurry contains three components, it presents problems in that both the amount of water and the amount of air can alter the apparent slurry density. By measuring density alone, the actual dry blend of cement and additives verses water ratio is not known since both water and air can cause the density to be altered. As an example, a first slurry with a measured density which is measured at low or atmospheric pressure may have exactly the correct cement to water ratio. However, a second slurry may have the same density as the first one, but because the second one contains a different amount of entrained air, the second slurry will have a ratio of dry blend of cement and additives verses water that will be in error.
Three ways have been and are currently being used to solve this problem. The first way is to use a high pressure downhole densitometer on the downstream side of the high pressure pumps that are used to pump slurry downhole. The second way is to use a pressurized mud cup measuring instrument. The third way is to use an average offset.
The first way is to use a high pressure downhole densitometer on the downstream side of the high pressure pumps that are used to pump slurry downhole. This point of measurement usually has a high enough pressure to eliminate most the effects of air entrainment on density measurement. However, a densitometer that is capable of measurement at high pressure employs a radioactive source. Measurement with this device is limited in accuracy, requires frequent calibration, and has a slow response time. In addition, this type device is undesirable due to the regulatory requirements associated with using a radioactive device. Also, this point of measurement is far enough downstream of the mixing system that its measured value could not be used for continuous control purposes because of further time delay.
The second way is to use a pressurized mud cup. This method is described in the 1972 Society of Petroleum Engineers of AIME Paper Number SPE 4092 entitled An Instrument for Measuring the Density of Air Entrained Fluids authored by S. K. Nickles of Halliburton Services. The pressurized mud cup is a device that requires a sample of the slurry from the mixing tub and then uses that sample to determine the density of the slurry under pressure. The accuracy of this device is limited to the skill of the operator. In addition, this is not a continuous measurement device. It takes a minimum of 3 minutes to take the sample and make the measurement. Thus, this device is not suitable for use for continuous density control. It can only be used as a spot check on the system density.
The third way is to use an average offset. Commonly, density is measured with radioactive or non-radioactive devices in the recirculation line of the mixing system. Since it is known that the slurry will always have some air entrainment, the operator will typically use an estimated average offset to compensate for the air entrainment. The amount of offset may be a guess or can be better estimated by comparing the circulating density measurement with the measurement produced by the pressurized mud cup testing described above. However, even if this estimate is determined from the pressurized mud cup measurement, it is not real time and slurry mixing conditions are constantly changing in a well cementing operation.
The present invention addresses the shortcomings of the prior methods by providing a new solution to this density measurement problem. This new solution obtains density measurements of a slurry at two different pressures and then uses the two density measurements and the two pressure measurements to compute absolute density of the slurry employing the following formula.Dabs=D1/(1−((D1/D2−1)/((P1/P2)1/n−1)))Where:    Dabs=absolute density    D1=first density    D2=second density    P1=absolute pressure at which the first density was measured    P2=absolute pressure at which the second density was measured    n=exponent for pressure-volume polytropic process relationship, P1×V1n=P2 ×V2n 
The fluid slurry passing through the densitometers illustrated in FIGS. 1-4 and FIGS. 7 and 8 can be chaacterized as an isothermal process where the entrained air is expanded and compressed at a near constant temperature. For an isothermal process, “n” can be assumed to be equal to 1.0 for air compression up to several hundred psi. With this assumption, the formula for Dabs becomes simplified to:Dabs=D1/(1−((D1/D2−1)/(P1/P2−1)))
The calculation employs the ideal gas model for an isothermal or constant temperature process to determine the behavior of entrained gas in a liquid or slurry. Also, for the purposes of this discussion, absolute pressure refers to the pressure measured relative to absolute zero pressure or the pressure that would occur at absolute vacuum. Absolute pressure is the sum of gauge pressure and atmospheric pressure.
For other fluids containing entrained gas where a value of “n”=1.0 is not adequate for accurate calculations, the following procedure can be used to experimentally determine “n”. Lay off successive values of P & V, measured at chosen points on the curve under investigation, on logarithmic cross-section paper; or, lay off values of log P and Log V on ordinary cross-section paper. If “n” is a constant, the points will lie in a straight line, and the slope of the line gives the value of n. If two representative points P1, V1 and P2, V2 be chosen, then n=(log P1−log P2)/(log V2−log V1). Several pairs of points should be used to test the constancy of n.” This procedure was taken from the Ref. Mechanical Engineers Handbook, Sixth Edition, McGraw-Hill Book Company, Inc. More complex mathematical models can be developed for curve fitting experimental data for “n”.
U.S. Pat. No. 7,117,717 issued to Wade M. Mattar teaches varying the pressure in an oscillating manner to produce a sinusoidal pressure curve and then using this data to calculate density by picking a P1 and D1 at a point where their values are at their lowest in the oscillation and pick P2 and D2 at the highest point of oscillation. The approach employed by is problematic for several reasons.
First, the approach does not maximize the pressure differences between P1 and P2, and therefore does not produce the most accurate absolute density Dabs calculation.
Mattar's approach is also problematic in that the measurement is continuously changing on a regular basis so a steady state is never realized for measurement purposes. This is particularly true when the fluid is cement slurry since the measurement of cement slurry is not smooth due to the non-homogeneous nature of this type of slurry. If the approach were employed with cement slurry, the sinusoidal curve would have an irregular saw-tooth appearance superimposed onto the sinusoid and trying to pick a valid, reproducible value from this data would be difficult. Although the Mattar approach could possible work if the fluid being measured was very homogeneous, it would not work well with a non-homogeneous slurry such as cement which contains solids, liquids and gases in varying ratios.
An additional problem with the Mattar approach involves bridging of cement slurry. When cement slurry passes through a valve that is being throttled, it will tend to stop up or bridge over the valve opening. The reason for this is that the flow restriction as the valve is being throttled tends to squeeze the water out of the cement slurry and the remaining cement tends to form a plug that stops up the valve.